Ruggero Vaia, CNR-ISC Firenze #
Transmitting a quantum state over an arbirarily long uniform channel with 
almost perfect quality #
An effective one-dimensional hopping model can be realized in several 
systems, such as spin chains, arrays of quantum dots or optical lattices. 
Each site of the array can be thought of as a `qubit', i.e. an object 
endowed with a 2-dimensional Hilbert space of states, and the natural 
dynamics of such an open chain of qubits can be exploited for transferring 
a quantum state between its ends, a task which is required for connecting 
registers in a quantum computer. Indeed, assuming that the first qubit is 
initially in a given state, the purpose of state transfer is that the 
dynamics of the chain leads at some time the same state to belong to the 
qubit sitting on the opposite end.
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In a uniform chain (with uniform hopping amplitudes) the quantum-transfer 
process is found to be impossible due the effect of dispersion. It is 
known that perfect transmission can occur if the hopping amplitudes are 
properly modulated along the channel; however, such an engineered setup is 
not likely to be realizable in a lab.
<br/>
Therefore we consider a chain with uniform hopping amplitudes and just 
allow the two extremal pairs of them to be weaker. Surprisingly, provided 
that the extremal couplings have suitable optimal values depending on the 
channel length, our setup gives an extremely high transfer quality, with 
average fidelity larger that 0.99 even in the limit of an infinitely long 
channel. The transmission time is ballistic and the quality of quantum 
transfer keeps being high in a large neighborhood of the optimal values so 
there is no need to finely tune the extremal hopping amplitudes in an 
experiment.